Background of Web Design

The most fundamental aspect of design - communication-based problem solving for a client - exists logically prior to the choice of media in which the problem might be solved. And while the INTERNET and the web are innovative, they and their associated design practices draw heavily on the existing knowledge. The domains and skill from which web design draw are extensive.
The design of graphical user interface for software, which encompasses screen-based tools with user interact, IA a close precursor to web design. Anyone who has used a computer for some time will be familiar, perhaps unconsciously, with the conversions in this kind of design.

The other similarity with software is that web site generally require the assistance of software engineers to be able to move from design solution to implementation. However, software is very task oriented and tends to focus on the document work area at which tools appear (a 'bring me' model). The web, by contest, is broader in its applications, and these are often more content-led and less task-centric (think of an online newspaper) and it's client -server model mandates a 'go to', rather than the 'bring me', model in which users have to move to a new page with every action. Library science and information design are closer precursor here.
Product design also has a lot in common with web design.

Like software, products tend to be task-oriented, though they interface with the user in more dimensions to communicate what they can do and how they can be used. Like the web, product design and development is more likely to be a core business activity than print non-linear narrative where user can freely navigate through the game 'content', and even manipulate or change it.
In another imagination-driven area of our culture, film and other time-based media bring to web design an understanding of narrative and story-telling, scene-setting and changing. pace and drama. (Ted Nelson argued that "interaction deign is a subset of film-making".) These characteristics will be more important for web design as the INTERNET becomes useful beyond its initial commercial applications.

Back in the world of commercial design, the mastery of visual communication and typography inform design for the web, particularly at the level of the text and image driven page. The particular skills associated with information design are also invaluable for creating intelligible and usable products given design and thus require more extensive negotiation - with, among others, engineering, sales and marketing, customer support and many other parts of the organization
Both product and software design (ans thus web design) draw on knowledge of the humans physical and psychological abilities and limitations.

Physical aspects are addressed by ergonomics and the psychological by human cognition and, in the case of computing, by human-computer interaction (HCI). The design of the mouse or of a keyboard is the ergonomics's focus, while the human cognition expert would have a view on how many items in a menu someone could take in, or the time it would take for a user to lose focuser to begin feeling frustrated waiting for a web page to load.